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olga55 [171]
2 years ago
6

Carlos is 5 less than 3 times his brother's age. Carlos' age is also 11 years older than his brother's age. How old is Carlos?​

Mathematics
1 answer:
mafiozo [28]2 years ago
8 0
<h2>Systems of Equations Word Problems</h2>

To solve these questions, we can translate key words into operations.

  • <em>Older</em> = add
  • <em>Less</em> <em>than</em> = subtract

<h2>Solving the Question</h2>

We're given:

  • Carlos' age is 5 less than 3 times his brother's age
  • Carlos' age is 11 years higher than his brother's age

There are two variables present in this problem: Carlos' age and his brother's age.

  • Let Carlos' age equal <em>x</em>
  • Let his brother's age equal <em>y</em>

Translate the given information into equations:

  • Carlos' age is 5 less than 3 times his brother's age
    ⇒ 3y-5=x
  • Carlos' age is 11 years higher than his brother's age
    ⇒ y+11=x

We can solve for <em>y</em>, his brothers age, using substitution:

3y-5=y+11\\2y=16\\y=8

Now, solve for <em>x</em> by substituting <em>y</em> in either of the equations:

y+11=x\\8+11=x\\x=19

Therefore, Carlos is 19 years old.

<h2>Answer</h2>

Carlos is 19 years old.

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